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Improved kernel estimation of copulas: Weak convergence and goodness-of-fit testing
- Source :
- Ann. Statist. 37, no. 5B (2009), 3023-3058
- Publication Year :
- 2009
- Publisher :
- The Institute of Mathematical Statistics, 2009.
-
Abstract
- We reconsider the existing kernel estimators for a copula function, as proposed in Gijbels and Mielniczuk [Comm. Statist. Theory Methods 19 (1990) 445--464], Fermanian, Radulovi\v{c} and Wegkamp [Bernoulli 10 (2004) 847--860] and Chen and Huang [Canad. J. Statist. 35 (2007) 265--282]. All of these estimators have as a drawback that they can suffer from a corner bias problem. A way to deal with this is to impose rather stringent conditions on the copula, outruling as such many classical families of copulas. In this paper, we propose improved estimators that take care of the typical corner bias problem. For Gijbels and Mielniczuk [Comm. Statist. Theory Methods 19 (1990) 445--464] and Chen and Huang [Canad. J. Statist. 35 (2007) 265--282], the improvement involves shrinking the bandwidth with an appropriate functional factor; for Fermanian, Radulovi\v{c} and Wegkamp [Bernoulli 10 (2004) 847--860], this is done by using a transformation. The theoretical contribution of the paper is a weak convergence result for the three improved estimators under conditions that are met for most copula families. We also discuss the choice of bandwidth parameters, theoretically and practically, and illustrate the finite-sample behaviour of the estimators in a simulation study. The improved estimators are applied to goodness-of-fit testing for copulas.<br />Comment: Published in at http://dx.doi.org/10.1214/08-AOS666 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
- Subjects :
- Statistics and Probability
Shrinkage estimator
goodness-of-fit
Kernel density estimation
Cramér–von Mises statistics
Mathematics - Statistics Theory
Statistics Theory (math.ST)
62G07 (Primary), 62G20 (Secondary)
copula
Cram´er-von Mises statistics
Gaussian process
goodness-offit
Copula (probability theory)
Goodness of fit
parametric bootstrap
Kendall’s tau
FOS: Mathematics
pseudo-observations
62G07
Applied mathematics
62G20
Mathematics
Weak convergence
Estimator
Kernel method
Copula
Kernel (statistics)
Kolmogorov–Smirnov statistics
weak convergence
Statistics, Probability and Uncertainty
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Ann. Statist. 37, no. 5B (2009), 3023-3058
- Accession number :
- edsair.doi.dedup.....958fb1289fc4d1b3ff10e66a8a30851c